S7_Notebook.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "library(lme4)\n",
    "options(rgl.useNULL=TRUE)\n",
    "library(LMERConvenienceFunctions)\n",
    "\n",
    "library(ggplot2)\n",
    "options(jupyter.plot_mimetypes = 'image/png')\n",
    "library(repr)\n",
    "options(repr.plot.width=6, repr.plot.height=6)\n",
    "\n",
    "library(car)\n",
    "library(MASS)\n",
    "\n",
    "library(vcd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Score\n",
    "\n",
    "In this notebook, we document our various steps taken to study the effect of the course of a session on the score a comment receives. Note that we only do this on a sample of 1 mio. data points here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = read.csv(\"/home/psinger/Reddit-depletion/data/sample.csv\", header=TRUE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1000000"
      ],
      "text/latex": [
       "1000000"
      ],
      "text/markdown": [
       "1000000"
      ],
      "text/plain": [
       "[1] 1000000"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nrow(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data inspection\n",
    "\n",
    "We start by getting a better feeling of our data. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can limit our data to those sessions that have at least two and less than 11 comments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "idx = data$session_comments > 1 & data$session_comments < 11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = data[idx,]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "515196"
      ],
      "text/latex": [
       "515196"
      ],
      "text/markdown": [
       "515196"
      ],
      "text/plain": [
       "[1] 515196"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nrow(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(data$score)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(data$score[data$score<10&data$score>-10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression model\n",
    "\n",
    "We use mixed-effects models where in the basic form (that we analyze in this notebook), we are interested in studying score ~ 1 + session_index + session_comments + (1|author)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear mixed-effects regression\n",
    "\n",
    "We start with a linear mixed-effects model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "m_lmer = lmer(score~1+session_index + session_comments+(1|author), data=data, REML=FALSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by maximum likelihood  ['lmerMod']\n",
       "Formula: score ~ 1 + session_index + session_comments + (1 | author)\n",
       "   Data: data\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 5497695  5497751 -2748843  5497685   515191 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-25.258  -0.100  -0.083  -0.053 110.277 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " author   (Intercept)   18.74   4.329  \n",
       " Residual             2504.33  50.043  \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                 Estimate Std. Error t value\n",
       "(Intercept)       6.22975    0.14724   42.31\n",
       "session_index    -0.38838    0.05266   -7.38\n",
       "session_comments  0.14978    0.04063    3.69\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) sssn_n\n",
       "session_ndx -0.175       \n",
       "sssn_cmmnts -0.538 -0.652"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m_lmer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mcp.fnc(m_lmer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What we can see in above plot is, that the residuals do not appear to be normally distributed and we can see clear heteroskedasticity. Thus, a linear model does not provide a good fit here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear mixed-effects regression (log-transform)\n",
    "\n",
    "Next, let us take the log of the response variable and repeat a linear regression. However, we first add a constant to the data in order to make all outcomes positive."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "-1267"
      ],
      "text/latex": [
       "-1267"
      ],
      "text/markdown": [
       "-1267"
      ],
      "text/plain": [
       "[1] -1267"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min(data$score)\n",
    "data$score.t = data$score + abs(min(data$score))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "m_lmer_log = lmer(log1p(score.t)~1+session_index+session_comments+(1|author), data=data, REML=FALSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by maximum likelihood  ['lmerMod']\n",
       "Formula: log1p(score.t) ~ 1 + session_index + session_comments + (1 |  \n",
       "    author)\n",
       "   Data: data\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       "-2256429 -2256373  1128219 -2256439   515191 \n",
       "\n",
       "Scaled residuals: \n",
       "     Min       1Q   Median       3Q      Max \n",
       "-261.979   -0.127   -0.105   -0.062   61.584 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance  Std.Dev.\n",
       " author   (Intercept) 1.123e-05 0.003351\n",
       " Residual             7.225e-04 0.026879\n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                   Estimate Std. Error t value\n",
       "(Intercept)       7.150e+00  7.948e-05   89954\n",
       "session_index    -2.361e-04  2.839e-05      -8\n",
       "session_comments  7.838e-05  2.193e-05       4\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) sssn_n\n",
       "session_ndx -0.174       \n",
       "sssn_cmmnts -0.538 -0.652"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m_lmer_log)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mcp.fnc(m_lmer_log)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That does not look satisfying at all. We should focus on generalized mixed-effects models to better model the count data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Poisson GLMER\n",
    "\n",
    "Let us start with a Poisson GLMER, which is a main choice when working with count data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00317215 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    }
   ],
   "source": [
    "m_poisson = glmer(score.t~1+session_index+session_comments+(1|author),data=data,family=poisson())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: score.t ~ 1 + session_index + session_comments + (1 | author)\n",
       "   Data: data\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 5286971  5287016 -2643482  5286963   515192 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-31.801  -0.092  -0.067  -0.026  90.279 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance  Std.Dev.\n",
       " author (Intercept) 0.0002952 0.01718 \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                   Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)       7.149e+00  9.572e-05   74692  < 2e-16 ***\n",
       "session_index    -3.098e-04  3.248e-05     -10  < 2e-16 ***\n",
       "session_comments  1.054e-04  2.568e-05       4 4.08e-05 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) sssn_n\n",
       "session_ndx -0.165       \n",
       "sssn_cmmnts -0.523 -0.637\n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 0.00317215 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m_poisson)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(fitted(m_poisson),resid(m_poisson))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The convergence message shows low magnitude and for such large data this might be a false positive as emphasized in the lme4 docu. \n",
    "\n",
    "The residual plots for generalized linear models are generally quite difficult to interpret as the residuals do not necessarily need to follow a normal distribution any longer. However, the fitted vs. residual plots shows a typical pattern for Poisson regression with curvilinear traces. What we can do though as a first step here, is to look at overdispersion (see http://glmm.wikidot.com/faq)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "overdisp_fun <- function(model) {\n",
    "  ## number of variance parameters in \n",
    "  ##   an n-by-n variance-covariance matrix\n",
    "  vpars <- function(m) {\n",
    "    nrow(m)*(nrow(m)+1)/2\n",
    "  }\n",
    "  model.df <- sum(sapply(VarCorr(model),vpars))+length(fixef(model))\n",
    "  rdf <- nrow(model.frame(model))-model.df\n",
    "  rp <- residuals(model,type=\"pearson\")\n",
    "  Pearson.chisq <- sum(rp^2)\n",
    "  prat <- Pearson.chisq/rdf\n",
    "  pval <- pchisq(Pearson.chisq, df=rdf, lower.tail=FALSE)\n",
    "  c(chisq=Pearson.chisq,ratio=prat,rdf=rdf,p=pval)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>chisq</dt>\n",
       "\t\t<dd>502883.576881925</dd>\n",
       "\t<dt>ratio</dt>\n",
       "\t\t<dd>0.97610905620026</dd>\n",
       "\t<dt>rdf</dt>\n",
       "\t\t<dd>515192</dd>\n",
       "\t<dt>p</dt>\n",
       "\t\t<dd>1</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[chisq] 502883.576881925\n",
       "\\item[ratio] 0.97610905620026\n",
       "\\item[rdf] 515192\n",
       "\\item[p] 1\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "chisq\n",
       ":   502883.576881925ratio\n",
       ":   0.97610905620026rdf\n",
       ":   515192p\n",
       ":   1\n",
       "\n"
      ],
      "text/plain": [
       "       chisq        ratio          rdf            p \n",
       "5.028836e+05 9.761091e-01 5.151920e+05 1.000000e+00 "
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "overdisp_fun(m_poisson)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It does not seem that we have any problem with overdispersion here.\n",
    "\n",
    "Let us be sure and check it with the dispersion_glmer function from the blmeco packages. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1.00454113384361"
      ],
      "text/latex": [
       "1.00454113384361"
      ],
      "text/markdown": [
       "1.00454113384361"
      ],
      "text/plain": [
       "[1] 1.004541"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "library(\"blmeco\") \n",
    "dispersion_glmer(m_poisson)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The value is between 0.75 and 1.4 which gives an indicator that there is no overdispersion problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, for completeness, we fit a negative binomial regression with quasi likelihood."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#just for initialization\n",
    "init = glm.nb(score.t~1+session_index+session_comments,data=data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "2636.65298197502"
      ],
      "text/latex": [
       "2636.65298197502"
      ],
      "text/markdown": [
       "2636.65298197502"
      ],
      "text/plain": [
       "[1] 2636.653"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "init$theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "iteration 1\n"
     ]
    }
   ],
   "source": [
    "m_pql_nb = glmmPQL(score.t~1+session_index, random = list(~1 | author), data = data, family = negative.binomial(theta=init$theta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed-effects model fit by maximum likelihood\n",
       " Data: data \n",
       "  AIC BIC logLik\n",
       "   NA  NA     NA\n",
       "\n",
       "Random effects:\n",
       " Formula: ~1 | author\n",
       "        (Intercept) Residual\n",
       "StdDev: 0.003408434 1.151876\n",
       "\n",
       "Variance function:\n",
       " Structure: fixed weights\n",
       " Formula: ~invwt \n",
       "Fixed effects: score.t ~ 1 + session_index \n",
       "                  Value    Std.Error     DF  t-value p-value\n",
       "(Intercept)    7.149542 9.748272e-05 288628 73341.63       0\n",
       "session_index -0.000206 3.136380e-05 226566    -6.56       0\n",
       " Correlation: \n",
       "              (Intr)\n",
       "session_index -0.823\n",
       "\n",
       "Standardized Within-Group Residuals:\n",
       "         Min           Q1          Med           Q3          Max \n",
       "-25.24565198  -0.09913141  -0.08359083  -0.05338234 110.26378433 \n",
       "\n",
       "Number of Observations: 515196\n",
       "Number of Groups: 288629 "
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m_pql_nb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, very similar results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Final model choice"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given our extensive analysis regarding the appropriate model for our data, we can conclude that all have very similar conclusions, namely that the session_index has a negative effect on score. For the rest of this section, let us focus on Poisson regression that seems to be appropriate for this count data at hand."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Significance of effects"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have decided on a model, we want to extend our inference. First, we want to study the significance of the fixed effects as well as potential additional random effects. \n",
    "\n",
    "There are several options for determining the significance of a fixed effect on the model. For example, a common approach is to use the ratio of the slope to its standard error and then use a t-test for determining its significance. Alternatively, one can also use F-tests for contrasting simpler to more complex models. Both methods require a specification of the degrees of freedom though which is not trivial in mixed models; methods such as the Satterthwaite approximation or Kenward-Roger approximation can be used for that task. \n",
    "As stated in Baayen 2008, we can also directly use the t-statistics given to derive statistical significance. Because we have a huge dataset, a t-statistic above 2 can be regarded as significant at the 5\\% level in a two-tailed test. You can derive this directly from the results above.\n",
    "\n",
    "However, here, we follow an approach used for comparing models: the Bayesian Information Criterion (alternatively we could also work with AIC or LRT). Basically, the idea is to specify different (in this case nested) models that successively incorporate additional fixed or random effects and then compare their BIC scores. The lower the BIC, the better a model is (above a small threshold).\n",
    "\n",
    "The baseline model we start with is:\n",
    "\n",
    "score = 1 + (1|author)\n",
    "\n",
    "The reason why we incorporate the random effect for author from the beginning is that this is necessary based on the design of the experiment. Also, as pointed out in http://glmm.wikidot.com/faq, you should not compare the fit of a (g)lmer with one from a (g)lm.\n",
    "\n",
    "Okay, so let us get the BIC for the baseline model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00309017 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: score.t ~ 1 + (1 | author)\n",
       "   Data: data\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 5287064  5287087 -2643530  5287060   515194 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-31.791  -0.093  -0.071  -0.029  90.268 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance  Std.Dev.\n",
       " author (Intercept) 0.0002953 0.01718 \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "             Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept) 7.149e+00  5.325e-05  134260   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 0.00309017 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m1 = glmer(score.t~1+(1|author), data = data, family=poisson())\n",
    "summary(m1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, let us incorporate the index and session length individually."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00225972 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: score.t ~ 1 + session_index + (1 | author)\n",
       "   Data: data\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 5286986  5287019 -2643490  5286980   515193 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-31.797  -0.096  -0.067  -0.026  90.267 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance  Std.Dev.\n",
       " author (Intercept) 0.0002953 0.01718 \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)    7.149e+00  8.159e-05   87621   <2e-16 ***\n",
       "session_index -2.249e-04  2.505e-05      -9   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr)\n",
       "session_ndx -0.758\n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 0.00225972 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m2 = glmer(score.t~1+session_index+(1|author), data = data, family=poisson())\n",
    "summary(m2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00397523 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: score.t ~ 1 + session_comments + (1 | author)\n",
       "   Data: data\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 5287060  5287093 -2643527  5287054   515193 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-31.790  -0.094  -0.069  -0.029  90.263 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance  Std.Dev.\n",
       " author (Intercept) 0.0002953 0.01718 \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                   Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)       7.149e+00  9.440e-05   75731   <2e-16 ***\n",
       "session_comments -5.053e-05  1.980e-05      -3   0.0107 *  \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr)\n",
       "sssn_cmmnts -0.826\n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 0.00397523 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m3 = glmer(score.t~1+session_comments+(1|author), data = data, family=poisson())\n",
    "summary(m3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on the lower BIC we can see that the incorporation of the session_index improves our model, thus, we make inference on it (also the t-value indicates high significance). The session_comments alone are not significant; let's check incorporating both."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00317215 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: score.t ~ 1 + session_index + session_comments + (1 | author)\n",
       "   Data: data\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 5286971  5287016 -2643482  5286963   515192 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-31.801  -0.092  -0.067  -0.026  90.279 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance  Std.Dev.\n",
       " author (Intercept) 0.0002952 0.01718 \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                   Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)       7.149e+00  9.572e-05   74692  < 2e-16 ***\n",
       "session_index    -3.098e-04  3.248e-05     -10  < 2e-16 ***\n",
       "session_comments  1.054e-04  2.568e-05       4 4.08e-05 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) sssn_n\n",
       "session_ndx -0.165       \n",
       "sssn_cmmnts -0.523 -0.637\n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 0.00317215 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m4 = glmer(score.t~1+session_index+session_comments+(1|author), data = data, family=poisson())\n",
    "summary(m4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected based on our initial empirical analysis in the paper, both the session index and session length are important effects to incorporate. The significance for session_index is less pronounced though as for the other experiments; however, for the complete data reported in the paper, strong significiance is given.\n",
    "\n",
    "We stop at this point as our scope of interest is covered. However, one can arbitrarily extend the existing model.\n",
    "For example, one might also argue that it is necessary to incorporate a random effect for the intercept based on different subreddits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.0564161 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: score.t ~ 1 + session_index + session_comments + (1 | author) +  \n",
       "    (1 | subreddit)\n",
       "   Data: data\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 5284397  5284452 -2642193  5284387   515191 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-31.806  -0.102  -0.046  -0.002  90.232 \n",
       "\n",
       "Random effects:\n",
       " Groups    Name        Variance  Std.Dev.\n",
       " author    (Intercept) 2.898e-04 0.017022\n",
       " subreddit (Intercept) 2.640e-06 0.001625\n",
       "Number of obs: 515196, groups:  author, 288629; subreddit, 12041\n",
       "\n",
       "Fixed effects:\n",
       "                   Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)       7.148e+00  1.088e-04   65684   <2e-16 ***\n",
       "session_index    -3.228e-04  3.246e-05     -10   <2e-16 ***\n",
       "session_comments  7.380e-05  2.571e-05       3   0.0041 ** \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) sssn_n\n",
       "session_ndx -0.144       \n",
       "sssn_cmmnts -0.446 -0.635\n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 0.0564161 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m5 = glmer(score.t~1+session_index+session_comments+(1|author)+(1|subreddit), data = data, family=poisson())\n",
    "summary(m5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, the BIC shows an improvement in the model. Yet, the inference on the fixed effects does not change. For complexity reasons, we neglect the random effect for the subreddit for the complete data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Collinearity\n",
    "\n",
    "We also want to check for multicollinearity in our model; some explanations and code for checking that in lme4 is provided in https://hlplab.wordpress.com/2011/02/24/diagnosing-collinearity-in-lme4/."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "4.48954996169921"
      ],
      "text/latex": [
       "4.48954996169921"
      ],
      "text/markdown": [
       "4.48954996169921"
      ],
      "text/plain": [
       "[1] 4.48955"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "1.68117610385677"
      ],
      "text/latex": [
       "1.68117610385677"
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      "text/markdown": [
       "1.68117610385677"
      ],
      "text/plain": [
       "[1] 1.681176"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "source(\"../mer-utils.R\")\n",
    "kappa.mer(m4)\n",
    "max(vif.mer(m4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both the condition number and VIF show no reasons to be concerned about collinearity in this model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Length as random effect\n",
    "\n",
    "We have decided to incorporate the variation between different session lengths as a controlling covariate, however we might also incorporate it as a controlling random effect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 16.194 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: score.t ~ 1 + session_index + (1 | session_comments) + (1 | author)\n",
       "   Data: data\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 5287002  5287047 -2643497  5286994   515192 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-31.763  -0.095  -0.068  -0.025  89.944 \n",
       "\n",
       "Random effects:\n",
       " Groups           Name        Variance  Std.Dev.\n",
       " author           (Intercept) 3.003e-04 0.017330\n",
       " session_comments (Intercept) 1.211e-07 0.000348\n",
       "Number of obs: 515196, groups:  author, 288629; session_comments, 9\n",
       "\n",
       "Fixed effects:\n",
       "                Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)    7.150e+00  1.888e-04   37863   <2e-16 ***\n",
       "session_index -3.723e-04  3.447e-05     -11   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr)\n",
       "session_ndx -0.690\n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 16.194 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m4_control = glmer(score.t~1+session_index+(1|session_comments)+(1|author), data = data, family=poisson())\n",
    "summary(m4_control)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results are similar."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convergence problems\n",
    "\n",
    "Convergence warnings (which we partly also see for experiments on the complete data) are most likely false positives and do not effect the results. The gold standard approach to investigate this is to utilize different optimizers and compare the coefficients. If they are not similar, our inference is stable which is the case here. The code is based on Ben Bolkers code presented online: http://stackoverflow.com/questions/21344555/convergence-error-for-development-version-of-lme4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.0525527 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00803934 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?Warning message:\n",
      "In optimx.check(par, optcfg$ufn, optcfg$ugr, optcfg$uhess, lower, : Parameters or bounds appear to have different scalings.\n",
      "  This can cause poor performance in optimization. \n",
      "  It is important for derivative free methods like BOBYQA, UOBYQA, NEWUOA.Warning message:\n",
      "In optwrap(optimizer, devfun, start, rho$lower, control = control, : convergence code 1 from optimxWarning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 1.00577 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?Warning message:\n",
      "In optimx.check(par, optcfg$ufn, optcfg$ugr, optcfg$uhess, lower, : Parameters or bounds appear to have different scalings.\n",
      "  This can cause poor performance in optimization. \n",
      "  It is important for derivative free methods like BOBYQA, UOBYQA, NEWUOA.Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.540356 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 2.25709 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00446455 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    }
   ],
   "source": [
    "g0.bobyqa <- glmer(score.t~1+session_index+session_comments+(1|author),\n",
    "      family = poisson, data = data,\n",
    "                   control=glmerControl(optimizer=\"bobyqa\"))\n",
    "g0.NM <- update(g0.bobyqa,control=glmerControl(optimizer=\"Nelder_Mead\"))\n",
    "library(optimx)\n",
    "g0.nlminb <- update(g0.bobyqa,control=glmerControl(optimizer=\"optimx\",\n",
    "                              optCtrl=list(method=\"nlminb\")))\n",
    "g0.LBFGSB <- update(g0.bobyqa,control=glmerControl(optimizer=\"optimx\",\n",
    "                              optCtrl=list(method=\"L-BFGS-B\")))\n",
    "\n",
    "library(nloptr)\n",
    "## from https://github.com/lme4/lme4/issues/98:\n",
    "defaultControl <- list(algorithm=\"NLOPT_LN_BOBYQA\",xtol_rel=1e-6,maxeval=1e5)\n",
    "nloptwrap2 <- function(fn,par,lower,upper,control=list(),...) {\n",
    "    for (n in names(defaultControl)) \n",
    "      if (is.null(control[[n]])) control[[n]] <- defaultControl[[n]]\n",
    "    res <- nloptr(x0=par,eval_f=fn,lb=lower,ub=upper,opts=control,...)\n",
    "    with(res,list(par=solution,\n",
    "                  fval=objective,\n",
    "                  feval=iterations,\n",
    "                  conv=if (status>0) 0 else status,\n",
    "                  message=message))\n",
    "}\n",
    "g0.bobyqa2 <- update(g0.bobyqa,control=glmerControl(optimizer=nloptwrap2))\n",
    "g0.NM2 <- update(g0.bobyqa,control=glmerControl(optimizer=nloptwrap2,\n",
    "                           optCtrl=list(algorithm=\"NLOPT_LN_NELDERMEAD\")))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "getpar <- function(x) c(getME(x,c(\"theta\")),fixef(x))\n",
    "modList <- list(bobyqa=g0.bobyqa,NM=g0.NM,nlminb=g0.nlminb,\n",
    "                bobyqa2=g0.bobyqa2,NM2=g0.NM2,LBFGSB=g0.LBFGSB)\n",
    "ctab <- sapply(modList,getpar)\n",
    "library(reshape2)\n",
    "mtab <- melt(ctab)\n",
    "library(ggplot2)\n",
    "theme_set(theme_bw())\n",
    "ggplot(mtab,aes(x=Var2,y=value,colour=Var2))+\n",
    "    geom_point()+facet_wrap(~Var1,scale=\"free\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Randomized baseline data\n",
    "\n",
    "In order to finally confirm our intuition and inference on the negative effect of the session index on the number of responses, we also study our randomized baseline data. We basically have two different randomized datasets: (i) new sessions based on randomized time differences and (ii) randomized positions inside existing sessions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "idx = data$session_comments_random > 1\n",
    "data_random = data[idx,]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.0017097 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: score.t ~ 1 + (1 | author)\n",
       "   Data: data_random\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 3993292  3993314 -1996644  3993288   388336 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-26.714  -0.091  -0.069  -0.027  88.683 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance  Std.Dev.\n",
       " author (Intercept) 0.0003202 0.0179  \n",
       "Number of obs: 388338, groups:  author, 216454\n",
       "\n",
       "Fixed effects:\n",
       "             Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept) 7.149e+00  6.248e-05  114424   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 0.0017097 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m1_random = glmer(score.t~1+(1|author), data = data_random, family=poisson())\n",
    "summary(m1_random)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.0055438 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: score.t ~ 1 + session_index_random + (1 | author)\n",
       "   Data: data_random\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 3993293  3993326 -1996644  3993287   388335 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-26.712  -0.092  -0.069  -0.028  88.683 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance  Std.Dev.\n",
       " author (Intercept) 0.0003202 0.0179  \n",
       "Number of obs: 388338, groups:  author, 216454\n",
       "\n",
       "Fixed effects:\n",
       "                       Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)           7.149e+00  7.553e-05   94645   <2e-16 ***\n",
       "session_index_random -1.678e-05  1.471e-05      -1    0.254    \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr)\n",
       "sssn_ndx_rn -0.562\n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 0.0055438 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m2_random = glmer(score.t~1+session_index_random+(1|author), data = data_random, family=poisson())\n",
    "summary(m2_random)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.0351677 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: score.t ~ 1 + session_comments_random + (1 | author)\n",
       "   Data: data_random\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 3993294  3993327 -1996644  3993288   388335 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-26.715  -0.091  -0.069  -0.028  88.684 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance  Std.Dev.\n",
       " author (Intercept) 0.0003202 0.0179  \n",
       "Number of obs: 388338, groups:  author, 216454\n",
       "\n",
       "Fixed effects:\n",
       "                         Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)             7.149e+00  7.792e-05   91743   <2e-16 ***\n",
       "session_comments_random 3.044e-06  9.735e-06       0    0.755    \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr)\n",
       "sssn_cmmnt_ -0.598\n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 0.0351677 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m3_random = glmer(score.t~1+session_comments_random+(1|author), data = data_random, family=poisson())\n",
    "summary(m3_random)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.0216727 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: score.t ~ 1 + session_index_random + session_comments_random +  \n",
       "    (1 | author)\n",
       "   Data: data_random\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 3993292  3993336 -1996642  3993284   388334 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-26.711  -0.091  -0.069  -0.028  88.685 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance  Std.Dev.\n",
       " author (Intercept) 0.0003202 0.0179  \n",
       "Number of obs: 388338, groups:  author, 216454\n",
       "\n",
       "Fixed effects:\n",
       "                          Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)              7.149e+00  7.888e-05   90633   <2e-16 ***\n",
       "session_index_random    -4.349e-05  2.162e-05      -2   0.0442 *  \n",
       "session_comments_random  2.414e-05  1.431e-05       2   0.0916 .  \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) sssn_n_\n",
       "sssn_ndx_rn -0.155        \n",
       "sssn_cmmnt_ -0.288 -0.733 \n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 0.0216727 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m4_random = glmer(score.t~1+session_index_random+session_comments_random+(1|author), data = data_random, family=poisson())\n",
    "summary(m4_random)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When comparing m3_random and m4_random, we can see now is that the incorporation of the session index is not improving the model in terms of the BIC score  and is thus, not significant (also has a low t-value < 2). \n",
    "\n",
    "The reason why the session length itself is still significant can be explained by our very conservative randomization method that just randomizes the time differences between comments before sessionizing and thus, still keeps many sessions intact."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Randomized indexes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00397523 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: score.t ~ 1 + session_comments + (1 | author)\n",
       "   Data: data\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 5287060  5287093 -2643527  5287054   515193 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-31.790  -0.094  -0.069  -0.029  90.263 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance  Std.Dev.\n",
       " author (Intercept) 0.0002953 0.01718 \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                   Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)       7.149e+00  9.440e-05   75731   <2e-16 ***\n",
       "session_comments -5.053e-05  1.980e-05      -3   0.0107 *  \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr)\n",
       "sssn_cmmnts -0.826\n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 0.00397523 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m3_random_2 = glmer(score.t~1+session_comments+(1|author), data = data, family=poisson())\n",
    "summary(m3_random_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00529796 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: score.t ~ 1 + session_index_random_2 + session_comments + (1 |  \n",
       "    author)\n",
       "   Data: data\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 5287061  5287106 -2643527  5287053   515192 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-31.791  -0.094  -0.069  -0.029  90.263 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance  Std.Dev.\n",
       " author (Intercept) 0.0002953 0.01718 \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                         Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)             7.149e+00  9.581e-05   74614   <2e-16 ***\n",
       "session_index_random_2  2.269e-05  3.252e-05       1   0.4854    \n",
       "session_comments       -6.185e-05  2.560e-05      -2   0.0157 *  \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) ss___2\n",
       "sssn_ndx__2 -0.171       \n",
       "sssn_cmmnts -0.521 -0.634\n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 0.00529796 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m4_random_2 = glmer(score.t~1+session_index_random_2+session_comments+(1|author), data = data, family=poisson())\n",
    "summary(m4_random_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, we see similar behavior, the incorporation of the random session index does not improve the model compared to one that already includes the session length."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Overall, the analyses presented in this notebook have demonstrated that the course of a session has a (negative) effect on the score a post receives."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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